TSTP Solution File: LAT026-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n021.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 : Sun Jul 17 07:14:48 EDT 2022
% Result : Unsatisfiable 0.90s 1.30s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT026-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : woody %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 16:56:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.56/0.97 ********************************************************************************
% 0.56/0.97 * W A L D M E I S T E R \| \ / \|/ *
% 0.56/0.97 * |/ | \/ | *
% 0.56/0.97 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.56/0.97 * A. Jaeger and B. Loechner | | *
% 0.56/0.97 * <waldmeister@informatik.uni-kl.de> | *
% 0.56/0.97 ********************************************************************************
% 0.56/0.97
% 0.56/0.97
% 0.56/0.97 Goals:
% 0.56/0.97 ------
% 0.56/0.97
% 0.56/0.97 ( 1) meet(meet(a,b),c) ?=? meet(a,meet(b,c))
% 0.56/0.97
% 0.56/0.97 Detected structure: Orkus
% 0.56/0.97 ********************************************************************************
% 0.56/0.97 ****************************** COMPLETION - PROOF ******************************
% 0.56/0.97 ********************************************************************************
% 0.56/0.97
% 0.90/1.30 joined goal: 1 meet(meet(a,b),c) ?= meet(a,meet(b,c)) to meet(a,meet(c,b))
% 0.90/1.30 goal joined
% 0.90/1.30 % SZS status Unsatisfiable
% 0.90/1.30 #START OF PROOF
% 0.90/1.30 % SZS output start CNFRefutation
% 0.90/1.30 cnf('0.1.0.0',axiom,
% 0.90/1.30 ( X1 = join(X1,X1) ),
% 0.90/1.30 file('/tmp/WALDMEISTER_27629_n021')).
% 0.90/1.30 cnf('0.1.1.0',plain,
% 0.90/1.30 ( X1 = join(X1,X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.90/1.30 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.90/1.30 cnf('0.1.2.0',plain,
% 0.90/1.30 ( join(X1,X1) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_1]).
% 0.90/1.30 cnf('0.2.0.0',axiom,
% 0.90/1.30 ( X1 = join(join(meet(X2,X1),meet(X3,X1)),X1) ),
% 0.90/1.30 file('/tmp/WALDMEISTER_27629_n021')).
% 0.90/1.30 cnf('0.2.1.0',plain,
% 0.90/1.30 ( X1 = join(join(meet(X2,X1),meet(X3,X1)),X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.90/1.30 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.2.2.0',plain,
% 0.90/1.30 ( join(join(meet(X1,X2),meet(X3,X2)),X2) = X2 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_2]).
% 0.90/1.30 cnf('0.4.0.0',axiom,
% 0.90/1.30 ( X1 = meet(X1,join(X2,join(X1,X3))) ),
% 0.90/1.30 file('/tmp/WALDMEISTER_27629_n021')).
% 0.90/1.30 cnf('0.4.1.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(X2,join(X1,X3))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.90/1.30 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.4.2.0',plain,
% 0.90/1.30 ( meet(X1,join(X2,join(X1,X3))) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_4]).
% 0.90/1.30 cnf('0.5.0.0',axiom,
% 0.90/1.30 ( X1 = meet(meet(join(X2,X1),join(X3,X1)),X1) ),
% 0.90/1.30 file('/tmp/WALDMEISTER_27629_n021')).
% 0.90/1.30 cnf('0.5.1.0',plain,
% 0.90/1.30 ( X1 = meet(meet(join(X2,X1),join(X3,X1)),X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.90/1.30 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.90/1.30 cnf('0.5.2.0',plain,
% 0.90/1.30 ( meet(meet(join(X1,X2),join(X3,X2)),X2) = X2 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.5.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_5]).
% 0.90/1.30 cnf('0.6.0.0',axiom,
% 0.90/1.30 ( join(X1,X2) = join(X2,X1) ),
% 0.90/1.30 file('/tmp/WALDMEISTER_27629_n021')).
% 0.90/1.30 cnf('0.6.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(X2,X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.90/1.30 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.90/1.30 cnf('0.6.2.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(X2,X1) ),
% 0.90/1.30 inference(activate,[status(thm)],['0.6.1.0']),
% 0.90/1.30 [equation_1]).
% 0.90/1.30 cnf('0.7.0.0',axiom,
% 0.90/1.30 ( meet(X1,X2) = meet(X2,X1) ),
% 0.90/1.30 file('/tmp/WALDMEISTER_27629_n021')).
% 0.90/1.30 cnf('0.7.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(X2,X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.90/1.30 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.90/1.30 cnf('0.7.2.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(X2,X1) ),
% 0.90/1.30 inference(activate,[status(thm)],['0.7.1.0']),
% 0.90/1.30 [equation_2]).
% 0.90/1.30 cnf('0.8.0.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(X1,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.4.2.0','0.1.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.8.1.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(X1,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.90/1.30 [weight('<41,4,1,[1,0,0,2]>')]).
% 0.90/1.30 cnf('0.8.2.0',plain,
% 0.90/1.30 ( meet(X1,join(X1,X2)) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.8.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_6]).
% 0.90/1.30 cnf('0.9.0.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(X2,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.4.2.0','0.1.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.9.1.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.90/1.30 [weight('<41,4,1,[1,0,0,4]>')]).
% 0.90/1.30 cnf('0.9.2.0',plain,
% 0.90/1.30 ( meet(X1,join(X2,X1)) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_7]).
% 0.90/1.30 cnf('0.10.0.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(join(X1,X2),X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.4.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.10.1.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(join(X1,X2),X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.10.0.0']),
% 0.90/1.30 [weight('<71,6,4,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.10.2.0',plain,
% 0.90/1.30 ( meet(X1,join(join(X1,X2),X3)) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.10.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_8]).
% 0.90/1.30 cnf('0.11.0.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.4.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.11.1.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(X2,join(X3,X1))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.90/1.30 [weight('<71,6,4,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.11.2.0',plain,
% 0.90/1.30 ( meet(X1,join(X2,join(X3,X1))) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_9]).
% 0.90/1.30 cnf('0.12.0.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(join(X2,X1),X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.10.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.12.1.0',plain,
% 0.90/1.30 ( X1 = meet(X1,join(join(X2,X1),X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.12.0.0']),
% 0.90/1.30 [weight('<71,10,6,[1,0,0,3]>')]).
% 0.90/1.30 cnf('0.12.2.0',plain,
% 0.90/1.30 ( meet(X1,join(join(X2,X1),X3)) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.12.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_10]).
% 0.90/1.30 cnf('0.13.0.0',plain,
% 0.90/1.30 ( join(join(meet(X1,X2),meet(X3,X2)),X2) = X2 ),
% 0.90/1.30 inference(interreduction_right,[status(thm)],['0.2.2.0'])).
% 0.90/1.30 cnf('0.13.1.0',plain,
% 0.90/1.30 ( join(join(meet(X1,X2),meet(X3,X2)),X2) = X2 ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.90/1.30 [weight('<109,2,6,[0,0,0,0]>')]).
% 0.90/1.30 cnf('0.13.1.1',plain,
% 0.90/1.30 ( join(X2,join(meet(X1,X2),meet(X3,X2))) = X2 ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.13.1.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.13.2.0',plain,
% 0.90/1.30 ( join(X1,join(meet(X2,X1),meet(X3,X1))) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.13.1.1',theory(equality)]),
% 0.90/1.30 [u,rule_11]).
% 0.90/1.30 cnf('0.14.0.0',plain,
% 0.90/1.30 ( X1 = join(X1,meet(X2,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.13.2.0','0.1.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.14.1.0',plain,
% 0.90/1.30 ( X1 = join(X1,meet(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.90/1.30 [weight('<41,13,1,[1,0,0,2]>')]).
% 0.90/1.30 cnf('0.14.2.0',plain,
% 0.90/1.30 ( join(X1,meet(X2,X1)) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_12]).
% 0.90/1.30 cnf('0.15.0.0',plain,
% 0.90/1.30 ( X1 = join(X1,meet(X1,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.14.2.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.15.1.0',plain,
% 0.90/1.30 ( X1 = join(X1,meet(X1,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.15.0.0']),
% 0.90/1.30 [weight('<41,14,7,[1,0,0,2]>')]).
% 0.90/1.30 cnf('0.15.2.0',plain,
% 0.90/1.30 ( join(X1,meet(X1,X2)) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.15.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_13]).
% 0.90/1.30 cnf('0.19.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),X1) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.9.2.0','0.15.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.19.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.19.0.0']),
% 0.90/1.30 [weight('<53,15,9,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.19.1.1',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(X1,meet(X1,X2)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.19.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.19.2.0',plain,
% 0.90/1.30 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.19.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_17]).
% 0.90/1.30 cnf('0.20.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.11.2.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.20.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.20.0.0']),
% 0.90/1.30 [weight('<87,14,11,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.20.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),join(X3,X2)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.20.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_18]).
% 0.90/1.30 cnf('0.21.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X2,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.12.2.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.21.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X2,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.21.0.0']),
% 0.90/1.30 [weight('<87,14,12,[0,0,0,3]>')]).
% 0.90/1.30 cnf('0.21.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),join(X2,X3)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.21.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_19]).
% 0.90/1.30 cnf('0.22.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.11.2.0','0.15.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.22.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.90/1.30 [weight('<87,15,11,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.22.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),join(X3,X1)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.22.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_20]).
% 0.90/1.30 cnf('0.23.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X1,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.12.2.0','0.15.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.23.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X1,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.90/1.30 [weight('<87,15,12,[0,0,0,3]>')]).
% 0.90/1.30 cnf('0.23.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),join(X1,X3)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_21]).
% 0.90/1.30 cnf('0.25.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),meet(X3,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.14.2.0','0.20.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.25.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),meet(X3,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.90/1.30 [weight('<87,20,14,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.25.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),meet(X3,X2)) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_23]).
% 0.90/1.30 cnf('0.26.0.0',plain,
% 0.90/1.30 ( join(X1,meet(X2,X1)) = join(X1,meet(X3,meet(X2,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.25.2.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.26.0.1',plain,
% 0.90/1.30 ( X1 = join(X1,meet(X3,meet(X2,X1))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.26.0.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.26.1.0',plain,
% 0.90/1.30 ( X1 = join(X1,meet(X3,meet(X2,X1))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.26.0.1']),
% 0.90/1.30 [weight('<71,25,14,[1,0,0,1]>')]).
% 0.90/1.30 cnf('0.26.2.0',plain,
% 0.90/1.30 ( join(X1,meet(X2,meet(X3,X1))) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_24]).
% 0.90/1.30 cnf('0.28.0.0',plain,
% 0.90/1.30 ( X1 = join(X1,meet(meet(X2,X1),X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.26.2.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.28.1.0',plain,
% 0.90/1.30 ( X1 = join(X1,meet(meet(X2,X1),X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.28.0.0']),
% 0.90/1.30 [weight('<71,26,7,[1,0,0,2]>')]).
% 0.90/1.30 cnf('0.28.2.0',plain,
% 0.90/1.30 ( join(X1,meet(meet(X2,X1),X3)) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.28.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_26]).
% 0.90/1.30 cnf('0.35.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),meet(X1,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.14.2.0','0.23.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.35.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),meet(X1,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.35.0.0']),
% 0.90/1.30 [weight('<87,23,14,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.35.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),meet(X1,X3)) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.35.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_33]).
% 0.90/1.30 cnf('0.39.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(meet(X1,X3),join(X1,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.35.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.39.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(meet(X1,X3),join(X1,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.39.0.0']),
% 0.90/1.30 [weight('<87,35,6,[1,0,0,0]>')]).
% 0.90/1.30 cnf('0.39.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),join(X1,X3)) = join(X1,X3) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.39.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_37]).
% 0.90/1.30 cnf('0.48.0.0',plain,
% 0.90/1.30 ( meet(meet(join(X1,X2),join(X3,X2)),X2) = X2 ),
% 0.90/1.30 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 0.90/1.30 cnf('0.48.1.0',plain,
% 0.90/1.30 ( meet(meet(join(X1,X2),join(X3,X2)),X2) = X2 ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.48.0.0']),
% 0.90/1.30 [weight('<109,5,7,[0,0,0,0]>')]).
% 0.90/1.30 cnf('0.48.1.1',plain,
% 0.90/1.30 ( meet(X2,meet(join(X1,X2),join(X3,X2))) = X2 ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.48.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.48.2.0',plain,
% 0.90/1.30 ( meet(X1,meet(join(X2,X1),join(X3,X1))) = X1 ),
% 0.90/1.30 inference(orient,[status(thm)],['0.48.1.1',theory(equality)]),
% 0.90/1.30 [u,rule_46]).
% 0.90/1.30 cnf('0.56.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X2,meet(X4,join(X1,join(X2,X3))))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.13.2.0','0.4.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.56.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X2,meet(X4,join(X1,join(X2,X3))))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.56.0.0']),
% 0.90/1.30 [weight('<?,13,4,[1,0,0,3]>')]).
% 0.90/1.30 cnf('0.56.2.0',plain,
% 0.90/1.30 ( join(join(X1,join(X2,X3)),join(X2,meet(X4,join(X1,join(X2,X3))))) = join(X1,join(X2,X3)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_54]).
% 0.90/1.30 cnf('0.107.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(X1,meet(X3,join(X1,X2)))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.13.2.0','0.8.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.107.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(X1,meet(X3,join(X1,X2)))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.107.0.0']),
% 0.90/1.30 [weight('<?,13,8,[1,0,0,3]>')]).
% 0.90/1.30 cnf('0.107.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X1,meet(X3,join(X1,X2)))) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.107.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_105]).
% 0.90/1.30 cnf('0.108.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(X1,meet(X3,X2))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.107.2.0','0.20.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.108.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(X1,meet(X3,X2))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.108.0.0']),
% 0.90/1.30 [weight('<129,107,20,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.108.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.108.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_106]).
% 0.90/1.30 cnf('0.110.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X2,X1),join(X1,meet(X3,X2))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.108.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.110.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X2,X1),join(X1,meet(X3,X2))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.110.0.0']),
% 0.90/1.30 [weight('<129,108,6,[1,0,0,1]>')]).
% 0.90/1.30 cnf('0.110.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X2,meet(X3,X1))) = join(X2,X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.110.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_108]).
% 0.90/1.30 cnf('0.112.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = meet(join(X1,X2),join(X2,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.8.2.0','0.110.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.112.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = meet(join(X1,X2),join(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.112.0.0']),
% 0.90/1.30 [weight('<87,110,8,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.112.2.0',plain,
% 0.90/1.30 ( meet(join(X1,X2),join(X2,X1)) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.112.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_110]).
% 0.90/1.30 cnf('0.113.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(meet(X3,X2),X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.108.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.113.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(meet(X3,X2),X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.113.0.0']),
% 0.90/1.30 [weight('<129,108,6,[1,0,0,4]>')]).
% 0.90/1.30 cnf('0.113.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(meet(X3,X2),X1)) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.113.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_111]).
% 0.90/1.30 cnf('0.117.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X2,X1),join(meet(X3,X2),X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.110.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.117.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X2,X1),join(meet(X3,X2),X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.117.0.0']),
% 0.90/1.30 [weight('<129,110,6,[1,0,0,4]>')]).
% 0.90/1.30 cnf('0.117.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(meet(X3,X1),X2)) = join(X2,X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.117.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_115]).
% 0.90/1.30 cnf('0.151.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X2,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.56.2.0','0.8.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.151.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.151.0.0']),
% 0.90/1.30 [weight('<149,56,8,[1,0,0,8]>')]).
% 0.90/1.30 cnf('0.151.1.1',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X2,X1),join(X1,join(X2,X3))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.151.1.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.151.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X2,join(X1,X3))) = join(X2,join(X1,X3)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.151.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_149]).
% 0.90/1.30 cnf('0.152.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = meet(join(X1,X2),join(X2,join(X1,X3))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.8.2.0','0.151.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.152.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = meet(join(X1,X2),join(X2,join(X1,X3))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.152.0.0']),
% 0.90/1.30 [weight('<129,151,8,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.152.2.0',plain,
% 0.90/1.30 ( meet(join(X1,X2),join(X2,join(X1,X3))) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.152.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_150]).
% 0.90/1.30 cnf('0.155.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = meet(join(X1,X2),join(X2,join(X3,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.152.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.155.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = meet(join(X1,X2),join(X2,join(X3,X1))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.155.0.0']),
% 0.90/1.30 [weight('<129,152,6,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.155.2.0',plain,
% 0.90/1.30 ( meet(join(X1,X2),join(X2,join(X3,X1))) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.155.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_153]).
% 0.90/1.30 cnf('0.158.0.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X3,X2)) = meet(join(meet(X1,X2),meet(X3,X2)),X2) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.9.2.0','0.13.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.158.1.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X3,X2)) = meet(join(meet(X1,X2),meet(X3,X2)),X2) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.158.0.0']),
% 0.90/1.30 [weight('<?,13,9,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.158.1.1',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),meet(X3,X2))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.158.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.158.2.0',plain,
% 0.90/1.30 ( meet(X1,join(meet(X2,X1),meet(X3,X1))) = join(meet(X2,X1),meet(X3,X1)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.158.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_156]).
% 0.90/1.30 cnf('0.161.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X1,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.107.2.0','0.4.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.161.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X1,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.161.0.0']),
% 0.90/1.30 [weight('<149,107,4,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.161.1.1',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,X2),join(X1,join(X2,X3))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.161.1.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.161.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X1,join(X2,X3))) = join(X1,join(X2,X3)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.161.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_159]).
% 0.90/1.30 cnf('0.162.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X1,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.107.2.0','0.11.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.162.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X1,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.162.0.0']),
% 0.90/1.30 [weight('<149,107,11,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.162.1.1',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,X3),join(X1,join(X2,X3))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.162.1.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.162.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X1,join(X3,X2))) = join(X1,join(X3,X2)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.162.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_160]).
% 0.90/1.30 cnf('0.172.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X3,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.113.2.0','0.9.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.172.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(X3,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.172.0.0']),
% 0.90/1.30 [weight('<149,113,9,[1,0,0,5]>')]).
% 0.90/1.30 cnf('0.172.1.1',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X3,X1),join(X1,join(X2,X3))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.172.1.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.172.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X2,join(X3,X1))) = join(X2,join(X3,X1)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.172.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_170]).
% 0.90/1.30 cnf('0.175.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(join(X2,X3),X1),join(X3,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.117.2.0','0.9.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.175.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(join(X2,X3),X1),join(X3,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.175.0.0']),
% 0.90/1.30 [weight('<149,117,9,[1,0,0,5]>')]).
% 0.90/1.30 cnf('0.175.1.1',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X3,X1),join(join(X2,X3),X1)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.175.1.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.175.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(join(X3,X1),X2)) = join(X2,join(X3,X1)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.175.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_173]).
% 0.90/1.30 cnf('0.177.0.0',plain,
% 0.90/1.30 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X2,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.155.2.0','0.39.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.177.1.0',plain,
% 0.90/1.30 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.177.0.0']),
% 0.90/1.30 [weight('<149,155,39,[1,0,0,4]>')]).
% 0.90/1.30 cnf('0.177.1.1',plain,
% 0.90/1.30 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,meet(X2,X3))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.177.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.177.2.0',plain,
% 0.90/1.30 ( meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.177.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_175]).
% 0.90/1.30 cnf('0.209.0.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(X2,meet(X3,join(X1,X2)))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.13.2.0','0.9.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.209.1.0',plain,
% 0.90/1.30 ( join(X1,X2) = join(join(X1,X2),join(X2,meet(X3,join(X1,X2)))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.209.0.0']),
% 0.90/1.30 [weight('<?,13,9,[1,0,0,3]>')]).
% 0.90/1.30 cnf('0.209.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X2,meet(X3,join(X1,X2)))) = join(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.209.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_207]).
% 0.90/1.30 cnf('0.210.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,join(X2,X3)),join(join(X2,X3),join(X2,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.209.2.0','0.152.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.210.0.1',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X2,X3),join(X2,X1)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.210.0.0','0.172.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.210.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X2,X3),join(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.210.0.1']),
% 0.90/1.30 [weight('<103,209,152,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.210.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X1,X3)) = join(X3,join(X1,X2)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.210.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_208]).
% 0.90/1.30 cnf('0.211.0.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X1,join(X2,X3))) = join(X1,join(X2,X3)) ),
% 0.90/1.30 inference(interreduction_right,[status(thm)],['0.161.2.0'])).
% 0.90/1.30 cnf('0.211.0.1',plain,
% 0.90/1.30 ( join(join(X2,X3),join(X1,X2)) = join(X1,join(X2,X3)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.211.0.0','0.210.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.211.1.0',plain,
% 0.90/1.30 ( join(join(X2,X3),join(X1,X2)) = join(X1,join(X2,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.211.0.1']),
% 0.90/1.30 [weight('<103,161,210,[0,0,0,0]>')]).
% 0.90/1.30 cnf('0.211.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X3,X1)) = join(X3,join(X1,X2)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.211.1.0',theory(equality)]),
% 0.90/1.30 [u,rule_209]).
% 0.90/1.30 cnf('0.212.0.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X1,join(X3,X2))) = join(X1,join(X3,X2)) ),
% 0.90/1.30 inference(interreduction_right,[status(thm)],['0.162.2.0'])).
% 0.90/1.30 cnf('0.212.0.1',plain,
% 0.90/1.30 ( join(join(X3,X2),join(X1,X2)) = join(X1,join(X3,X2)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.212.0.0','0.210.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.212.1.0',plain,
% 0.90/1.30 ( join(join(X3,X2),join(X1,X2)) = join(X1,join(X3,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.212.0.1']),
% 0.90/1.30 [weight('<103,162,210,[0,0,0,0]>')]).
% 0.90/1.30 cnf('0.212.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X3,X2)) = join(X3,join(X1,X2)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.212.1.0',theory(equality)]),
% 0.90/1.30 [u,rule_210]).
% 0.90/1.30 cnf('0.217.0.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(join(X3,X1),X2)) = join(X2,join(X3,X1)) ),
% 0.90/1.30 inference(interreduction_right,[status(thm)],['0.175.2.0'])).
% 0.90/1.30 cnf('0.217.0.1',plain,
% 0.90/1.30 ( join(join(X3,X1),join(X1,X2)) = join(X2,join(X3,X1)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.217.0.0','0.212.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.217.1.0',plain,
% 0.90/1.30 ( join(join(X3,X1),join(X1,X2)) = join(X2,join(X3,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.217.0.1']),
% 0.90/1.30 [weight('<103,175,212,[0,0,0,0]>')]).
% 0.90/1.30 cnf('0.217.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),join(X2,X3)) = join(X3,join(X1,X2)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.217.1.0',theory(equality)]),
% 0.90/1.30 [u,rule_215]).
% 0.90/1.30 cnf('0.218.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,X2),join(X2,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.211.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.218.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X1,X2),join(X2,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.218.0.0']),
% 0.90/1.30 [weight('<103,211,6,[1,0,0,0]>')]).
% 0.90/1.30 cnf('0.218.1.1',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.218.1.0','0.217.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.218.2.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(X3,join(X1,X2)) ),
% 0.90/1.30 inference(activate,[status(thm)],['0.218.1.1']),
% 0.90/1.30 [equation_3]).
% 0.90/1.30 cnf('0.219.0.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X3,X1),X2) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.218.2.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.219.1.0',plain,
% 0.90/1.30 ( join(X1,join(X2,X3)) = join(join(X3,X1),X2) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.219.0.0']),
% 0.90/1.30 [weight('<65,218,6,[1,0,0,0]>')]).
% 0.90/1.30 cnf('0.219.2.0',plain,
% 0.90/1.30 ( join(join(X1,X2),X3) = join(X2,join(X3,X1)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.219.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_216]).
% 0.90/1.30 cnf('0.232.0.0',plain,
% 0.90/1.30 ( join(X1,join(meet(X2,join(X3,X1)),X3)) = join(X3,X1) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.219.2.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.232.1.0',plain,
% 0.90/1.30 ( join(X1,join(meet(X2,join(X3,X1)),X3)) = join(X3,X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.232.0.0']),
% 0.90/1.30 [weight('<129,219,14,[1,0,0,0]>')]).
% 0.90/1.30 cnf('0.232.1.1',plain,
% 0.90/1.30 ( join(X1,join(X3,meet(X2,join(X3,X1)))) = join(X3,X1) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.232.1.0','0.6.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.232.2.0',plain,
% 0.90/1.30 ( join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X2,X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.232.1.1',theory(equality)]),
% 0.90/1.30 [u,rule_227]).
% 0.90/1.30 cnf('0.298.0.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X2,X1),meet(X3,X2))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.158.2.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.298.1.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X2,X1),meet(X3,X2))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.298.0.0']),
% 0.90/1.30 [weight('<169,158,7,[1,0,0,3]>')]).
% 0.90/1.30 cnf('0.298.2.0',plain,
% 0.90/1.30 ( meet(X1,join(meet(X1,X2),meet(X3,X1))) = join(meet(X2,X1),meet(X3,X1)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.298.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_291]).
% 0.90/1.30 cnf('0.299.0.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X2,X1),X2)) = meet(X2,meet(X2,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.298.2.0','0.15.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.299.0.1',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X2,X1),X2)) = meet(X2,X1) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.299.0.0','0.19.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.299.1.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X2,X1),X2)) = meet(X2,X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.299.0.1']),
% 0.90/1.30 [weight('<129,298,15,[1,0,0,2]>')]).
% 0.90/1.30 cnf('0.299.1.1',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X2,meet(X2,X1))) = meet(X2,X1) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.299.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.299.1.2',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.299.1.1','0.19.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.299.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X2,X1)) = meet(X2,X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.299.1.2',theory(equality)]),
% 0.90/1.30 [u,rule_292]).
% 0.90/1.30 cnf('0.300.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.8.2.0','0.299.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.300.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.300.0.0']),
% 0.90/1.30 [weight('<87,299,8,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.300.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,X1)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.300.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_293]).
% 0.90/1.30 cnf('0.301.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,meet(X2,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.4.2.0','0.299.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.301.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(X3,meet(X2,X1))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.301.0.0']),
% 0.90/1.30 [weight('<129,299,4,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.301.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),join(X3,meet(X2,X1))) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.301.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_294]).
% 0.90/1.30 cnf('0.303.0.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X2,X1),X3)) = meet(meet(X1,X2),join(meet(X1,X2),meet(meet(X2,X1),X3))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.177.2.0','0.299.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.303.0.1',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X2,X1),X3)) = meet(X1,X2) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.303.0.0','0.8.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.303.1.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X2,X1),X3)) = meet(X1,X2) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.303.0.1']),
% 0.90/1.30 [weight('<129,299,177,[0,0,0,1]>')]).
% 0.90/1.30 cnf('0.303.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X2,X1),X3)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.303.1.0',theory(equality)]),
% 0.90/1.30 [u,rule_296]).
% 0.90/1.30 cnf('0.304.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,X1)) = meet(meet(X1,X2),join(meet(X2,X1),X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.21.2.0','0.300.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.304.0.1',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(meet(X2,X1),X3)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.304.0.0','0.300.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.304.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),join(meet(X2,X1),X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.304.0.1']),
% 0.90/1.30 [weight('<129,300,21,[0,0,0,1]>')]).
% 0.90/1.30 cnf('0.304.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),join(meet(X2,X1),X3)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.304.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_297]).
% 0.90/1.30 cnf('0.305.0.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),X3) = join(X3,join(meet(X1,X2),meet(X2,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.232.2.0','0.304.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.305.0.1',plain,
% 0.90/1.30 ( join(meet(X1,X2),X3) = join(X3,meet(X2,X1)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.305.0.0','0.299.2.0',theory(equality)]),
% 0.90/1.30 [pos('R.2','L')]).
% 0.90/1.30 cnf('0.305.1.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),X3) = join(X3,meet(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.305.0.1']),
% 0.90/1.30 [weight('<120,304,232,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.305.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),X3) = join(X3,meet(X2,X1)) ),
% 0.90/1.30 inference(activate,[status(thm)],['0.305.1.0']),
% 0.90/1.30 [equation_8]).
% 0.90/1.30 cnf('0.311.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,join(X3,meet(X1,X2)))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.48.2.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.311.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,join(X3,meet(X1,X2)))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.311.0.0']),
% 0.90/1.30 [weight('<?,48,14,[1,0,0,3]>')]).
% 0.90/1.30 cnf('0.311.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.311.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_303]).
% 0.90/1.30 cnf('0.312.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(meet(X1,X2),X3),meet(X3,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.311.2.0','0.28.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.312.1.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(meet(X1,X2),X3),meet(X3,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.312.0.0']),
% 0.90/1.30 [weight('<149,311,28,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.312.1.1',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X3,X2),meet(meet(X1,X2),X3)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.312.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.312.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(meet(X3,X2),X1)) = meet(meet(X3,X2),X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.312.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_304]).
% 0.90/1.30 cnf('0.314.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,join(X2,X1)),X3) = meet(meet(X3,join(X2,X1)),meet(X1,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.312.2.0','0.9.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.314.0.1',plain,
% 0.90/1.30 ( meet(X1,X3) = meet(meet(X3,join(X2,X1)),meet(X1,X3)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.314.0.0','0.9.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.314.1.0',plain,
% 0.90/1.30 ( meet(X1,X3) = meet(meet(X3,join(X2,X1)),meet(X1,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.314.0.1']),
% 0.90/1.30 [weight('<129,312,9,[1,0,0,5]>')]).
% 0.90/1.30 cnf('0.314.1.1',plain,
% 0.90/1.30 ( meet(X1,X3) = meet(meet(X1,X3),meet(X3,join(X2,X1))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.314.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.314.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.314.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_306]).
% 0.90/1.30 cnf('0.315.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = join(meet(X1,X2),meet(meet(X3,X2),X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.15.2.0','0.312.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.315.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = join(meet(X1,X2),meet(meet(X3,X2),X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.315.0.0']),
% 0.90/1.30 [weight('<129,312,15,[0,0,0,2]>')]).
% 0.90/1.30 cnf('0.315.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X3,X2),X1)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.315.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_307]).
% 0.90/1.30 cnf('0.316.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),join(X3,X1)) = meet(meet(join(X3,X1),X2),meet(X1,X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.312.2.0','0.22.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.316.0.1',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(join(X3,X1),X2),meet(X1,X2)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.316.0.0','0.22.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.316.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(join(X3,X1),X2),meet(X1,X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.316.0.1']),
% 0.90/1.30 [weight('<129,312,22,[1,0,0,4]>')]).
% 0.90/1.30 cnf('0.316.1.1',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(join(X3,X1),X2)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.316.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.316.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(join(X3,X1),X2)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.316.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_308]).
% 0.90/1.30 cnf('0.318.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = join(meet(X1,X2),meet(meet(X3,X1),X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.303.2.0','0.312.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.318.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = join(meet(X1,X2),meet(meet(X3,X1),X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.318.0.0']),
% 0.90/1.30 [weight('<129,312,303,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.318.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(meet(X3,X1),X2)) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.318.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_310]).
% 0.90/1.30 cnf('0.320.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X2,X1),meet(X2,join(X3,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.314.2.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.320.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X2,X1),meet(X2,join(X3,X1))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.320.0.0']),
% 0.90/1.30 [weight('<129,314,7,[1,0,0,1]>')]).
% 0.90/1.30 cnf('0.320.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X2,X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.320.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_312]).
% 0.90/1.30 cnf('0.321.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = join(meet(X1,X2),meet(X1,meet(X3,X2))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.315.2.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.321.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = join(meet(X1,X2),meet(X1,meet(X3,X2))) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.321.0.0']),
% 0.90/1.30 [weight('<129,315,7,[1,0,0,4]>')]).
% 0.90/1.30 cnf('0.321.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(X1,meet(X3,X2))) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.321.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_313]).
% 0.90/1.30 cnf('0.323.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X2,X1),meet(join(X3,X1),X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.316.2.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.323.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X2,X1),meet(join(X3,X1),X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.323.0.0']),
% 0.90/1.30 [weight('<129,316,7,[1,0,0,1]>')]).
% 0.90/1.30 cnf('0.323.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(join(X3,X2),X1)) = meet(X2,X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.323.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_315]).
% 0.90/1.30 cnf('0.337.0.0',plain,
% 0.90/1.30 ( meet(X1,meet(X2,X3)) = meet(meet(X1,meet(X2,X3)),meet(X3,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.301.2.0','0.318.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.337.1.0',plain,
% 0.90/1.30 ( meet(X1,meet(X2,X3)) = meet(meet(X1,meet(X2,X3)),meet(X3,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.337.0.0']),
% 0.90/1.30 [weight('<149,318,301,[0,0,0,4]>')]).
% 0.90/1.30 cnf('0.337.1.1',plain,
% 0.90/1.30 ( meet(X1,meet(X2,X3)) = meet(meet(X3,X1),meet(X1,meet(X2,X3))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.337.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.337.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.337.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_329]).
% 0.90/1.30 cnf('0.338.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X3,meet(X1,X2)),meet(X3,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.320.2.0','0.15.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.338.1.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X3,meet(X1,X2)),meet(X3,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.338.0.0']),
% 0.90/1.30 [weight('<149,320,15,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.338.1.1',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X3,X1),meet(X3,meet(X1,X2))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.338.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.338.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(meet(X2,X3),X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.338.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_330]).
% 0.90/1.30 cnf('0.340.0.0',plain,
% 0.90/1.30 ( meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X1,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.321.2.0','0.9.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.340.1.0',plain,
% 0.90/1.30 ( meet(X1,join(X2,X3)) = join(meet(X1,join(X2,X3)),meet(X1,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.340.0.0']),
% 0.90/1.30 [weight('<149,321,9,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.340.1.1',plain,
% 0.90/1.30 ( meet(X1,join(X2,X3)) = join(meet(X1,X3),meet(join(X2,X3),X1)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.340.1.0','0.305.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.340.2.0',plain,
% 0.90/1.30 ( join(meet(X1,X2),meet(join(X3,X2),X1)) = meet(X1,join(X3,X2)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.340.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_332]).
% 0.90/1.30 cnf('0.343.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X3,meet(X1,X2)),meet(X1,X3)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.323.2.0','0.15.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.343.1.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X3,meet(X1,X2)),meet(X1,X3)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.343.0.0']),
% 0.90/1.30 [weight('<149,323,15,[1,0,0,5]>')]).
% 0.90/1.30 cnf('0.343.1.1',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X1,X3),meet(X3,meet(X1,X2))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.343.1.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.343.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,meet(X1,X3))) = meet(meet(X1,X3),X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.343.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_335]).
% 0.90/1.30 cnf('0.344.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(meet(X1,X3),meet(X3,meet(X2,X1))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.343.2.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.344.0.1',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(X3,meet(X2,X1)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.344.0.0','0.337.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.344.1.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(X3,meet(X2,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.344.0.1']),
% 0.90/1.30 [weight('<120,343,7,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.344.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(X3,meet(X2,X1)) ),
% 0.90/1.30 inference(activate,[status(thm)],['0.344.1.0']),
% 0.90/1.30 [equation_9]).
% 0.90/1.30 cnf('0.345.0.0',plain,
% 0.90/1.30 ( meet(X1,meet(join(X2,X3),join(X3,X2))) = meet(join(X3,X2),X1) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.344.2.0','0.112.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('0.345.0.1',plain,
% 0.90/1.30 ( meet(X1,join(X2,X3)) = meet(join(X3,X2),X1) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.345.0.0','0.112.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2','L')]).
% 0.90/1.30 cnf('0.345.1.0',plain,
% 0.90/1.30 ( meet(X1,join(X2,X3)) = meet(join(X3,X2),X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.345.0.1']),
% 0.90/1.30 [weight('<120,344,112,[1,0,0,1]>')]).
% 0.90/1.30 cnf('0.345.2.0',plain,
% 0.90/1.30 ( meet(X1,join(X2,X3)) = meet(join(X3,X2),X1) ),
% 0.90/1.30 inference(activate,[status(thm)],['0.345.1.0']),
% 0.90/1.30 [equation_10]).
% 0.90/1.30 cnf('0.355.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(join(X3,meet(X1,X2)),X2)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.48.2.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.355.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(join(X3,meet(X1,X2)),X2)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.355.0.0']),
% 0.90/1.30 [weight('<179,48,14,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.355.1.1',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.355.1.0','0.345.2.0',theory(equality)]),
% 0.90/1.30 [pos('R.2','R')]).
% 0.90/1.30 cnf('0.355.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.355.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_337]).
% 0.90/1.30 cnf('0.357.0.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,X2),meet(X2,meet(X1,join(X3,X2)))) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.355.2.0','0.340.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.2','L')]).
% 0.90/1.30 cnf('0.357.0.1',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,join(X3,X2)),X2) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.357.0.0','0.343.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.357.1.0',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(meet(X1,join(X3,X2)),X2) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.357.0.1']),
% 0.90/1.30 [weight('<87,355,340,[1,0,0,6]>')]).
% 0.90/1.30 cnf('0.357.1.1',plain,
% 0.90/1.30 ( meet(X1,X2) = meet(X2,meet(join(X3,X2),X1)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.357.1.0','0.344.2.0',theory(equality)]),
% 0.90/1.30 [pos('R','L')]).
% 0.90/1.30 cnf('0.357.2.0',plain,
% 0.90/1.30 ( meet(X1,meet(join(X2,X1),X3)) = meet(X3,X1) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.357.1.1',theory(equality)]),
% 0.90/1.30 [x,rule_339]).
% 0.90/1.30 cnf('0.360.0.0',plain,
% 0.90/1.30 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X3,X1)) ),
% 0.90/1.30 inference(cp,[status(thm)],['0.357.2.0','0.14.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.2.1','L')]).
% 0.90/1.30 cnf('0.360.1.0',plain,
% 0.90/1.30 ( meet(X1,meet(X2,X3)) = meet(meet(X2,X3),meet(X3,X1)) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.360.0.0']),
% 0.90/1.30 [weight('<103,357,14,[1,0,0,3]>')]).
% 0.90/1.30 cnf('0.360.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,X3)) = meet(X3,meet(X1,X2)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.360.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_342]).
% 0.90/1.30 cnf('0.361.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,meet(X1,X3))) = meet(meet(X1,X3),X2) ),
% 0.90/1.30 inference(interreduction_right,[status(thm)],['0.343.2.0'])).
% 0.90/1.30 cnf('0.361.0.1',plain,
% 0.90/1.30 ( meet(meet(X1,X3),meet(X1,X2)) = meet(meet(X1,X3),X2) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.361.0.0','0.360.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.361.1.0',plain,
% 0.90/1.30 ( meet(meet(X1,X3),meet(X1,X2)) = meet(meet(X1,X3),X2) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.361.0.1']),
% 0.90/1.30 [weight('<103,343,360,[0,0,0,0]>')]).
% 0.90/1.30 cnf('0.361.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X1,X3)) = meet(meet(X1,X2),X3) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.361.1.0',theory(equality)]),
% 0.90/1.30 [u,rule_343]).
% 0.90/1.30 cnf('0.363.0.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(meet(X2,X3),X1) ),
% 0.90/1.30 inference(interreduction_right,[status(thm)],['0.338.2.0'])).
% 0.90/1.30 cnf('0.363.0.1',plain,
% 0.90/1.30 ( meet(meet(X1,X2),meet(X2,X3)) = meet(meet(X2,X3),X1) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.363.0.0','0.361.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.363.0.2',plain,
% 0.90/1.30 ( meet(X3,meet(X1,X2)) = meet(meet(X2,X3),X1) ),
% 0.90/1.30 inference(reduction,[status(thm)],['0.363.0.1','0.360.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('0.363.1.0',plain,
% 0.90/1.30 ( meet(X3,meet(X1,X2)) = meet(meet(X2,X3),X1) ),
% 0.90/1.30 inference(weigh,[status(thm)],['0.363.0.2']),
% 0.90/1.30 [weight('<65,338,361,[0,0,0,0]>')]).
% 0.90/1.30 cnf('0.363.2.0',plain,
% 0.90/1.30 ( meet(meet(X1,X2),X3) = meet(X2,meet(X3,X1)) ),
% 0.90/1.30 inference(orient,[status(thm)],['0.363.1.0',theory(equality)]),
% 0.90/1.30 [x,rule_345]).
% 0.90/1.30 cnf('1.0.0.0',conjecture,
% 0.90/1.30 ( meet(meet(a,b),c) = meet(a,meet(b,c)) ),
% 0.90/1.30 file('/tmp/WALDMEISTER_27629_n021',conjecture_1)).
% 0.90/1.30 cnf('1.0.0.1',plain,
% 0.90/1.30 ( meet(meet(b,a),c) = meet(a,meet(b,c)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['1.0.0.0','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('L.1','L')]).
% 0.90/1.30 cnf('1.0.0.2',plain,
% 0.90/1.30 ( meet(meet(b,a),c) = meet(a,meet(c,b)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['1.0.0.1','0.7.2.0',theory(equality)]),
% 0.90/1.30 [pos('R.2','L')]).
% 0.90/1.30 cnf('1.0.0.3',plain,
% 0.90/1.30 ( meet(a,meet(c,b)) = meet(a,meet(c,b)) ),
% 0.90/1.30 inference(reduction,[status(thm)],['1.0.0.2','0.363.2.0',theory(equality)]),
% 0.90/1.30 [pos('L','L')]).
% 0.90/1.30 cnf('1.0.0.4',plain,
% 0.90/1.30 ( $true ),
% 0.90/1.30 inference(trivial,[status(thm)],['1.0.0.3',theory(equality)]),
% 0.90/1.30 [conjecture_1]).
% 0.90/1.30
% 0.90/1.30 Proved Goals:
% 0.90/1.30 No. 1: meet(meet(a,b),c) ?= meet(a,meet(b,c)) joined, current: meet(a,meet(c,b)) = meet(a,meet(c,b))
% 0.90/1.30 1 goal was specified, which was proved.
% 0.90/1.30 % SZS output end CNFRefutation
% 0.90/1.30 #END OF PROOF
% 0.90/1.30
% 0.90/1.30 Problem WALDMEISTER_27629_n021
% 0.90/1.30 CPs.gen 121903
% 0.90/1.30 CPs.reexp 0
% 0.90/1.30 Select 11886
% 0.90/1.30 R 345
% 0.90/1.30 E 18
% 0.90/1.30 vsize 6.4M
% 0.90/1.30 rss 4.0M
% 0.90/1.30 process.time 0.335s
% 0.90/1.30 wallclock.time 0.335s
% 0.90/1.30 status S
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 Waldmeister states: Goal proved.
% 0.90/1.30 % SZS status Unsatisfiable
%------------------------------------------------------------------------------