TSTP Solution File: LAT021-1 by Waldmeister---710
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%------------------------------------------------------------------------------
% File : Waldmeister---710
% Problem : LAT021-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : woody %s
% Computer : n020.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 07:14:46 EDT 2022
% Result : Unsatisfiable 0.62s 1.06s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT021-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : woody %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 30 03:11:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 * W A L D M E I S T E R \| \ / \|/ *
% 0.59/0.99 * |/ | \/ | *
% 0.59/0.99 * (C) 1994-2010 A. Buch and Th. Hillenbrand, \ / \ / *
% 0.59/0.99 * A. Jaeger and B. Loechner | | *
% 0.59/0.99 * <waldmeister@informatik.uni-kl.de> | *
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.59/0.99
% 0.59/0.99 Goals:
% 0.59/0.99 ------
% 0.59/0.99
% 0.59/0.99 ( 1) join(meet(a,b),meet(a,c)) ?=? meet(a,join(b,c))
% 0.59/0.99
% 0.59/0.99 Detected structure: Verband
% 0.59/0.99 ********************************************************************************
% 0.59/0.99 ****************************** COMPLETION - PROOF ******************************
% 0.59/0.99 ********************************************************************************
% 0.59/0.99
% 0.62/1.06 joined goal: 1 join(meet(a,b),meet(a,c)) ?= meet(a,join(b,c)) to meet(a,join(c,b))
% 0.62/1.06 goal joined
% 0.62/1.06 % SZS status Unsatisfiable
% 0.62/1.06 #START OF PROOF
% 0.62/1.06 % SZS output start CNFRefutation
% 0.62/1.06 cnf('0.1.0.0',axiom,
% 0.62/1.06 ( X1 = join(X1,X1) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.1.1.0',plain,
% 0.62/1.06 ( X1 = join(X1,X1) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.1.0.0']),
% 0.62/1.06 [weight('<0,0,0,[0,0,0,1]>')]).
% 0.62/1.06 cnf('0.1.2.0',plain,
% 0.62/1.06 ( join(X1,X1) = X1 ),
% 0.62/1.06 inference(orient,[status(thm)],['0.1.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_1]).
% 0.62/1.06 cnf('0.2.0.0',axiom,
% 0.62/1.06 ( X1 = meet(X1,X1) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.2.1.0',plain,
% 0.62/1.06 ( X1 = meet(X1,X1) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.2.0.0']),
% 0.62/1.06 [weight('<1,0,0,[0,0,0,2]>')]).
% 0.62/1.06 cnf('0.2.2.0',plain,
% 0.62/1.06 ( meet(X1,X1) = X1 ),
% 0.62/1.06 inference(orient,[status(thm)],['0.2.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_2]).
% 0.62/1.06 cnf('0.3.0.0',axiom,
% 0.62/1.06 ( join(X1,X2) = join(X2,X1) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.3.1.0',plain,
% 0.62/1.06 ( join(X1,X2) = join(X2,X1) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.3.0.0']),
% 0.62/1.06 [weight('<2,0,0,[0,0,0,3]>')]).
% 0.62/1.06 cnf('0.3.2.0',plain,
% 0.62/1.06 ( join(X1,X2) = join(X2,X1) ),
% 0.62/1.06 inference(activate,[status(thm)],['0.3.1.0']),
% 0.62/1.06 [equation_1]).
% 0.62/1.06 cnf('0.4.0.0',axiom,
% 0.62/1.06 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.4.1.0',plain,
% 0.62/1.06 ( join(X1,join(X2,X3)) = join(join(X1,X2),X3) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.4.0.0']),
% 0.62/1.06 [weight('<3,0,0,[0,0,0,4]>')]).
% 0.62/1.06 cnf('0.4.2.0',plain,
% 0.62/1.06 ( join(join(X1,X2),X3) = join(X1,join(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.4.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_3]).
% 0.62/1.06 cnf('0.5.0.0',axiom,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = join(join(X1,meet(X2,X3)),meet(join(X1,X2),X3)) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.5.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = join(join(X1,meet(X2,X3)),meet(join(X1,X2),X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.5.0.0']),
% 0.62/1.06 [weight('<4,0,0,[0,0,0,5]>')]).
% 0.62/1.06 cnf('0.5.1.1',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = join(X1,join(meet(X2,X3),meet(join(X1,X2),X3))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.5.1.0','0.4.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.5.2.0',plain,
% 0.62/1.06 ( join(X1,join(meet(X2,X3),meet(join(X1,X2),X3))) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.5.1.1',theory(equality)]),
% 0.62/1.06 [x,rule_4]).
% 0.62/1.06 cnf('0.6.0.0',axiom,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.6.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X1,meet(X2,X3)),join(X1,X2)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.6.0.0']),
% 0.62/1.06 [weight('<5,0,0,[0,0,0,6]>')]).
% 0.62/1.06 cnf('0.6.2.0',plain,
% 0.62/1.06 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.6.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_5]).
% 0.62/1.06 cnf('0.7.0.0',axiom,
% 0.62/1.06 ( join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.7.1.0',plain,
% 0.62/1.06 ( join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.7.0.0']),
% 0.62/1.06 [weight('<6,0,0,[0,0,0,7]>')]).
% 0.62/1.06 cnf('0.7.1.1',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.7.1.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.7.2.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.7.1.1',theory(equality)]),
% 0.62/1.06 [u,rule_6]).
% 0.62/1.06 cnf('0.8.0.0',axiom,
% 0.62/1.06 ( meet(X1,X2) = meet(X2,X1) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.8.1.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X2,X1) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.8.0.0']),
% 0.62/1.06 [weight('<7,0,0,[0,0,0,8]>')]).
% 0.62/1.06 cnf('0.8.2.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X2,X1) ),
% 0.62/1.06 inference(activate,[status(thm)],['0.8.1.0']),
% 0.62/1.06 [equation_2]).
% 0.62/1.06 cnf('0.9.0.0',axiom,
% 0.62/1.06 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020')).
% 0.62/1.06 cnf('0.9.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.9.0.0']),
% 0.62/1.06 [weight('<8,0,0,[0,0,0,9]>')]).
% 0.62/1.06 cnf('0.9.2.0',plain,
% 0.62/1.06 ( meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.9.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_7]).
% 0.62/1.06 cnf('0.11.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.9.2.0','0.2.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.11.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.11.0.0']),
% 0.62/1.06 [weight('<5,9,2,[1,0,0,1]>')]).
% 0.62/1.06 cnf('0.11.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X1,X2)) = meet(X1,X2) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.11.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_9]).
% 0.62/1.06 cnf('0.13.0.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.11.2.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.13.1.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,meet(X2,X1)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.13.0.0']),
% 0.62/1.06 [weight('<5,11,8,[1,0,0,2]>')]).
% 0.62/1.06 cnf('0.13.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,X1)) = meet(X1,X2) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.13.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_11]).
% 0.62/1.06 cnf('0.14.0.0',plain,
% 0.62/1.06 ( meet(X1,join(X1,X2)) = join(X1,meet(X1,join(X1,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.7.2.0','0.2.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.14.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X1,X2)) = join(X1,meet(X1,join(X1,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.14.0.0']),
% 0.62/1.06 [weight('<7,7,2,[1,0,0,1]>')]).
% 0.62/1.06 cnf('0.14.2.0',plain,
% 0.62/1.06 ( join(X1,meet(X1,join(X1,X2))) = meet(X1,join(X1,X2)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.14.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_12]).
% 0.62/1.06 cnf('0.17.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X1,X2),X3) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.9.2.0','0.13.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.17.0.1',plain,
% 0.62/1.06 ( meet(X1,meet(X2,meet(X1,X3))) = meet(meet(X1,X2),X3) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.17.0.0','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.17.0.2',plain,
% 0.62/1.06 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.17.0.1','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.17.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.17.0.2']),
% 0.62/1.06 [weight('<7,13,9,[0,0,0,1]>')]).
% 0.62/1.06 cnf('0.17.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.17.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_15]).
% 0.62/1.06 cnf('0.22.0.0',plain,
% 0.62/1.06 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(interreduction_right,[status(thm)],['0.6.2.0'])).
% 0.62/1.06 cnf('0.22.1.0',plain,
% 0.62/1.06 ( meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.22.0.0']),
% 0.62/1.06 [weight('<9,6,8,[0,0,0,0]>')]).
% 0.62/1.06 cnf('0.22.1.1',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.22.1.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.22.2.0',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.22.1.1',theory(equality)]),
% 0.62/1.06 [u,rule_20]).
% 0.62/1.06 cnf('0.23.0.0',plain,
% 0.62/1.06 ( join(X1,meet(X1,X2)) = meet(X1,join(X1,meet(X1,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.22.2.0','0.1.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.23.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X1,X2)) = meet(X1,join(X1,meet(X1,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.23.0.0']),
% 0.62/1.06 [weight('<7,22,1,[1,0,0,1]>')]).
% 0.62/1.06 cnf('0.23.2.0',plain,
% 0.62/1.06 ( meet(X1,join(X1,meet(X1,X2))) = join(X1,meet(X1,X2)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.23.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_21]).
% 0.62/1.06 cnf('0.25.0.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.7.2.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.25.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,join(X3,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.25.0.0']),
% 0.62/1.06 [weight('<9,7,3,[1,0,0,6]>')]).
% 0.62/1.06 cnf('0.25.2.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,join(X3,X2))) = meet(X1,join(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.25.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_23]).
% 0.62/1.06 cnf('0.26.0.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X2,X3))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.7.2.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.26.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X2,X3))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.26.0.0']),
% 0.62/1.06 [weight('<9,8,7,[0,0,0,1]>')]).
% 0.62/1.06 cnf('0.26.2.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.26.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_24]).
% 0.62/1.06 cnf('0.29.0.0',plain,
% 0.62/1.06 ( join(X1,join(meet(X1,join(X1,X2)),X3)) = join(meet(X1,join(X1,X2)),X3) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.4.2.0','0.14.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.29.1.0',plain,
% 0.62/1.06 ( join(X1,join(meet(X1,join(X1,X2)),X3)) = join(meet(X1,join(X1,X2)),X3) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.29.0.0']),
% 0.62/1.06 [weight('<9,14,4,[0,0,0,1]>')]).
% 0.62/1.06 cnf('0.29.2.0',plain,
% 0.62/1.06 ( join(X1,join(meet(X1,join(X1,X2)),X3)) = join(meet(X1,join(X1,X2)),X3) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.29.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_27]).
% 0.62/1.06 cnf('0.33.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(meet(X2,X3),X4)) = meet(X1,meet(X2,meet(X3,meet(X1,X4)))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.17.2.0','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.33.0.1',plain,
% 0.62/1.06 ( meet(X1,meet(X2,meet(X3,X4))) = meet(X1,meet(X2,meet(X3,meet(X1,X4)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.33.0.0','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.33.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,meet(X3,X4))) = meet(X1,meet(X2,meet(X3,meet(X1,X4)))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.33.0.1']),
% 0.62/1.06 [weight('<9,17,9,[1,0,0,2]>')]).
% 0.62/1.06 cnf('0.33.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,meet(X3,meet(X1,X4)))) = meet(X1,meet(X2,meet(X3,X4))) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.33.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_31]).
% 0.62/1.06 cnf('0.44.0.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,X2)) = meet(join(meet(X1,X2),X1),meet(X1,X2)) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.22.2.0','0.1.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.44.0.1',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(join(meet(X1,X2),X1),meet(X1,X2)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.44.0.0','0.1.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.44.1.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(join(meet(X1,X2),X1),meet(X1,X2)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.44.0.1']),
% 0.62/1.06 [weight('<9,22,1,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.44.1.1',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(meet(X1,X2),join(meet(X1,X2),X1)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.44.1.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.44.1.2',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,meet(X2,join(meet(X1,X2),X1))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.44.1.1','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.44.1.3',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,meet(X1,X2)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.44.1.2','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('R.2.2','L')]).
% 0.62/1.06 cnf('0.44.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X1,meet(X1,X2)))) = meet(X1,X2) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.44.1.3',theory(equality)]),
% 0.62/1.06 [x,rule_42]).
% 0.62/1.06 cnf('0.45.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X2,meet(X2,X1)))) = meet(X1,meet(X2,X1)) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.17.2.0','0.44.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.45.0.1',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X2,X1))) = meet(X1,meet(X2,X1)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.45.0.0','0.23.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.45.0.2',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X2,X1))) = meet(X1,X2) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.45.0.1','0.13.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.45.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X2,X1))) = meet(X1,X2) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.45.0.2']),
% 0.62/1.06 [weight('<7,44,17,[0,0,0,2]>')]).
% 0.62/1.06 cnf('0.45.2.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X2,X1))) = meet(X1,X2) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.45.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_43]).
% 0.62/1.06 cnf('0.46.0.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,join(X2,meet(X1,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.45.2.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.46.1.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,join(X2,meet(X1,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.46.0.0']),
% 0.62/1.06 [weight('<7,45,8,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.46.2.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X1,X2))) = meet(X1,X2) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.46.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_44]).
% 0.62/1.06 cnf('0.47.0.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,meet(X2,X3))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.22.2.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.47.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,meet(X2,X3))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.47.0.0']),
% 0.62/1.06 [weight('<9,22,3,[1,0,0,1]>')]).
% 0.62/1.06 cnf('0.47.2.0',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.47.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_45]).
% 0.62/1.06 cnf('0.50.0.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,meet(X3,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.22.2.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.50.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,meet(X3,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.50.0.0']),
% 0.62/1.06 [weight('<9,22,8,[1,0,0,6]>')]).
% 0.62/1.06 cnf('0.50.2.0',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.50.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_48]).
% 0.62/1.06 cnf('0.51.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(join(X1,meet(X1,X2)),X3)) = meet(join(X1,meet(X1,X2)),X3) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.9.2.0','0.23.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.51.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(join(X1,meet(X1,X2)),X3)) = meet(join(X1,meet(X1,X2)),X3) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.51.0.0']),
% 0.62/1.06 [weight('<9,23,9,[0,0,0,1]>')]).
% 0.62/1.06 cnf('0.51.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(join(X1,meet(X1,X2)),X3)) = meet(join(X1,meet(X1,X2)),X3) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.51.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_49]).
% 0.62/1.06 cnf('0.56.0.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X3,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.25.2.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.56.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(X1,join(X3,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.56.0.0']),
% 0.62/1.06 [weight('<9,25,8,[1,0,0,1]>')]).
% 0.62/1.06 cnf('0.56.2.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.56.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_54]).
% 0.62/1.06 cnf('0.61.0.0',plain,
% 0.62/1.06 ( join(meet(X1,join(X1,X2)),meet(join(X1,X2),join(X1,X3))) = join(X1,meet(join(X1,X2),join(X1,X3))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.29.2.0','0.26.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.61.0.1',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.61.0.0','0.26.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.61.1.0',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(X1,X3))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.61.0.1']),
% 0.62/1.06 [weight('<9,29,26,[1,0,0,2]>')]).
% 0.62/1.06 cnf('0.61.2.0',plain,
% 0.62/1.06 ( join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.61.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_59]).
% 0.62/1.06 cnf('0.70.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,meet(X3,X1)))) = meet(X1,meet(X2,meet(X1,X3))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.17.2.0','0.45.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.70.0.1',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,meet(X3,X1)))) = meet(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.70.0.0','0.17.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.70.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,meet(X3,X1)))) = meet(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.70.0.1']),
% 0.62/1.06 [weight('<9,45,17,[0,0,0,4]>')]).
% 0.62/1.06 cnf('0.70.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,meet(X3,X1)))) = meet(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.70.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_68]).
% 0.62/1.06 cnf('0.71.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(join(X2,X1),X2)) = meet(X1,join(X2,meet(X1,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.70.2.0','0.50.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.71.0.1',plain,
% 0.62/1.06 ( meet(X1,meet(join(X2,X1),X2)) = meet(X1,X2) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.71.0.0','0.46.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.71.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(join(X2,X1),X2)) = meet(X1,X2) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.71.0.1']),
% 0.62/1.06 [weight('<7,70,50,[1,0,0,2]>')]).
% 0.62/1.06 cnf('0.71.1.1',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X2,X1))) = meet(X1,X2) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.71.1.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.71.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X2,X1))) = meet(X1,X2) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.71.1.1',theory(equality)]),
% 0.62/1.06 [u,rule_69]).
% 0.62/1.06 cnf('0.72.0.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.71.2.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.72.1.0',plain,
% 0.62/1.06 ( meet(X1,X2) = meet(X1,meet(X2,join(X1,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.72.0.0']),
% 0.62/1.06 [weight('<7,71,3,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.72.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X1,X2))) = meet(X1,X2) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.72.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_70]).
% 0.62/1.06 cnf('0.81.0.0',plain,
% 0.62/1.06 ( meet(join(X1,meet(X1,X2)),join(meet(X1,X2),meet(X1,X3))) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.51.2.0','0.47.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.81.0.1',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.81.0.0','0.47.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.81.1.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X1,X3))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.81.0.1']),
% 0.62/1.06 [weight('<9,51,47,[1,0,0,2]>')]).
% 0.62/1.06 cnf('0.81.2.0',plain,
% 0.62/1.06 ( meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.81.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_79]).
% 0.62/1.06 cnf('0.85.0.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(join(X3,X2),X1)) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.56.2.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.85.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,X3)) = join(meet(X2,X1),meet(join(X3,X2),X1)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.85.0.0']),
% 0.62/1.06 [weight('<9,56,8,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.85.2.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(X2,join(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.85.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_83]).
% 0.62/1.06 cnf('0.86.0.0',plain,
% 0.62/1.06 ( join(X1,join(meet(X2,X3),meet(join(X1,X2),X3))) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(interreduction_right,[status(thm)],['0.5.2.0'])).
% 0.62/1.06 cnf('0.86.0.1',plain,
% 0.62/1.06 ( join(X1,meet(X3,join(X2,X1))) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.86.0.0','0.85.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.86.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X3,join(X2,X1))) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.86.0.1']),
% 0.62/1.06 [weight('<7,5,85,[0,0,0,0]>')]).
% 0.62/1.06 cnf('0.86.2.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,X2)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.86.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_84]).
% 0.62/1.06 cnf('0.89.0.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = join(X1,meet(X3,join(X1,X2))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.86.2.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.89.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = join(X1,meet(X3,join(X1,X2))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.89.0.0']),
% 0.62/1.06 [weight('<7,86,3,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.89.2.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.89.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_87]).
% 0.62/1.06 cnf('0.90.0.0',plain,
% 0.62/1.06 ( join(X1,meet(join(X1,X2),join(X1,X3))) = meet(join(X1,X2),join(X1,X3)) ),
% 0.62/1.06 inference(interreduction_right,[status(thm)],['0.61.2.0'])).
% 0.62/1.06 cnf('0.90.0.1',plain,
% 0.62/1.06 ( join(X1,meet(X3,join(X1,X2))) = meet(join(X1,X2),join(X1,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.90.0.0','0.89.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.90.0.2',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.90.0.1','0.89.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.90.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.90.0.2']),
% 0.62/1.06 [weight('<7,61,89,[0,0,0,0]>')]).
% 0.62/1.06 cnf('0.90.2.0',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.90.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_88]).
% 0.62/1.06 cnf('0.95.0.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,X3)) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.90.2.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.1','L')]).
% 0.62/1.06 cnf('0.95.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X1,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.95.0.0']),
% 0.62/1.06 [weight('<7,90,3,[1,0,0,1]>')]).
% 0.62/1.06 cnf('0.95.2.0',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X2,X3)) = join(X2,meet(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.95.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_93]).
% 0.62/1.06 cnf('0.99.0.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X3,X1)) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.95.2.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.99.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,X3)) = meet(join(X2,X1),join(X3,X1)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.99.0.0']),
% 0.62/1.06 [weight('<7,95,3,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.99.2.0',plain,
% 0.62/1.06 ( meet(join(X1,X2),join(X3,X2)) = join(X2,meet(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.99.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_97]).
% 0.62/1.06 cnf('0.109.0.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X3,X1))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.81.2.0','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.109.1.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),meet(X3,X1))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.109.0.0']),
% 0.62/1.06 [weight('<9,81,8,[1,0,0,6]>')]).
% 0.62/1.06 cnf('0.109.2.0',plain,
% 0.62/1.06 ( meet(X1,join(meet(X1,X2),meet(X3,X1))) = join(meet(X1,X2),meet(X1,X3)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.109.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_107]).
% 0.62/1.06 cnf('0.115.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(meet(X2,join(X3,X1)),join(X1,meet(X3,X2)))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.72.2.0','0.86.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.115.0.1',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(X2,meet(join(X3,X1),join(X1,meet(X3,X2))))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.115.0.0','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('R.2','L')]).
% 0.62/1.06 cnf('0.115.0.2',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(X2,join(X1,meet(X3,X2)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.115.0.1','0.47.2.0',theory(equality)]),
% 0.62/1.06 [pos('R.2.2','L')]).
% 0.62/1.06 cnf('0.115.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(X2,join(X1,meet(X3,X2)))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.115.0.2']),
% 0.62/1.06 [weight('<9,86,72,[0,0,0,4]>')]).
% 0.62/1.06 cnf('0.115.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X1,meet(X3,X2)))) = meet(X1,meet(X2,join(X3,X1))) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.115.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_112]).
% 0.62/1.06 cnf('0.118.0.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,meet(X3,X4))) = join(X1,meet(X3,meet(X4,join(X1,X2)))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.89.2.0','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.118.1.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,meet(X3,X4))) = join(X1,meet(X3,meet(X4,join(X1,X2)))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.118.0.0']),
% 0.62/1.06 [weight('<9,89,9,[1,0,0,2]>')]).
% 0.62/1.06 cnf('0.118.2.0',plain,
% 0.62/1.06 ( join(X1,meet(X2,meet(X3,join(X1,X4)))) = join(X1,meet(X4,meet(X2,X3))) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.118.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_115]).
% 0.62/1.06 cnf('0.156.0.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(X2,join(meet(X3,X2),X1))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.115.2.0','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.156.1.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(X3,X1))) = meet(X1,meet(X2,join(meet(X3,X2),X1))) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.156.0.0']),
% 0.62/1.06 [weight('<9,115,3,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.156.2.0',plain,
% 0.62/1.06 ( meet(X1,meet(X2,join(meet(X3,X2),X1))) = meet(X1,meet(X2,join(X3,X1))) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.156.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_150]).
% 0.62/1.06 cnf('0.157.0.0',plain,
% 0.62/1.06 ( meet(meet(X1,join(X2,X3)),meet(X1,join(X2,meet(X1,join(X2,X3))))) = meet(meet(X1,join(X2,X3)),meet(X1,meet(X1,join(X2,X3)))) ),
% 0.62/1.06 inference(cp,[status(thm)],['0.156.2.0','0.26.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.157.0.1',plain,
% 0.62/1.06 ( meet(X1,meet(join(X2,X3),meet(X1,join(X2,meet(X1,join(X2,X3)))))) = meet(meet(X1,join(X2,X3)),meet(X1,meet(X1,join(X2,X3)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.0','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.157.0.2',plain,
% 0.62/1.06 ( meet(X1,meet(join(X2,X3),join(X2,meet(X1,join(X2,X3))))) = meet(meet(X1,join(X2,X3)),meet(X1,meet(X1,join(X2,X3)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.1','0.17.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.157.0.3',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,meet(X1,join(X2,X3))))) = meet(meet(X1,join(X2,X3)),meet(X1,meet(X1,join(X2,X3)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.2','0.90.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.157.0.4',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,meet(X3,X1)))) = meet(meet(X1,join(X2,X3)),meet(X1,meet(X1,join(X2,X3)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.3','0.118.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('0.157.0.5',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(meet(X1,join(X2,X3)),meet(X1,meet(X1,join(X2,X3)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.4','0.11.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('0.157.0.6',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,meet(join(X2,X3),meet(X1,meet(X1,join(X2,X3))))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.5','0.9.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.157.0.7',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,meet(join(X2,X3),meet(X1,join(X2,X3)))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.6','0.33.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.157.0.8',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,meet(join(X2,X3),join(X2,X3))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.7','0.17.2.0',theory(equality)]),
% 0.62/1.06 [pos('R','L')]).
% 0.62/1.06 cnf('0.157.0.9',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X3,meet(X2,X2))) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.8','0.99.2.0',theory(equality)]),
% 0.62/1.06 [pos('R.2','L')]).
% 0.62/1.06 cnf('0.157.0.10',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X3,X2)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.157.0.9','0.2.2.0',theory(equality)]),
% 0.62/1.06 [pos('R.2.2','L')]).
% 0.62/1.06 cnf('0.157.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X3,X2)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.157.0.10']),
% 0.62/1.06 [weight('<7,156,26,[1,0,0,4]>')]).
% 0.62/1.06 cnf('0.157.2.0',plain,
% 0.62/1.06 ( meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X3,X2)) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.157.1.0',theory(equality)]),
% 0.62/1.06 [u,rule_151]).
% 0.62/1.06 cnf('0.158.0.0',plain,
% 0.62/1.06 ( meet(X1,join(meet(X1,X2),meet(X3,X1))) = join(meet(X1,X2),meet(X1,X3)) ),
% 0.62/1.06 inference(interreduction_right,[status(thm)],['0.109.2.0'])).
% 0.62/1.06 cnf('0.158.0.1',plain,
% 0.62/1.06 ( meet(X1,join(X3,meet(X1,X2))) = join(meet(X1,X2),meet(X1,X3)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['0.158.0.0','0.157.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('0.158.1.0',plain,
% 0.62/1.06 ( meet(X1,join(X3,meet(X1,X2))) = join(meet(X1,X2),meet(X1,X3)) ),
% 0.62/1.06 inference(weigh,[status(thm)],['0.158.0.1']),
% 0.62/1.06 [weight('<7,109,157,[0,0,0,0]>')]).
% 0.62/1.06 cnf('0.158.2.0',plain,
% 0.62/1.06 ( join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,meet(X1,X2))) ),
% 0.62/1.06 inference(orient,[status(thm)],['0.158.1.0',theory(equality)]),
% 0.62/1.06 [x,rule_152]).
% 0.62/1.06 cnf('1.0.0.0',conjecture,
% 0.62/1.06 ( join(meet(a,b),meet(a,c)) = meet(a,join(b,c)) ),
% 0.62/1.06 file('/tmp/WALDMEISTER_26129_n020',conjecture_1)).
% 0.62/1.06 cnf('1.0.0.1',plain,
% 0.62/1.06 ( meet(a,join(c,meet(a,b))) = meet(a,join(b,c)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['1.0.0.0','0.158.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('1.0.0.2',plain,
% 0.62/1.06 ( meet(a,join(c,meet(b,a))) = meet(a,join(b,c)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['1.0.0.1','0.8.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2.2','L')]).
% 0.62/1.06 cnf('1.0.0.3',plain,
% 0.62/1.06 ( meet(a,join(b,c)) = meet(a,join(b,c)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['1.0.0.2','0.157.2.0',theory(equality)]),
% 0.62/1.06 [pos('L','L')]).
% 0.62/1.06 cnf('1.0.0.4',plain,
% 0.62/1.06 ( meet(a,join(c,b)) = meet(a,join(b,c)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['1.0.0.3','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('L.2','L')]).
% 0.62/1.06 cnf('1.0.0.5',plain,
% 0.62/1.06 ( meet(a,join(c,b)) = meet(a,join(c,b)) ),
% 0.62/1.06 inference(reduction,[status(thm)],['1.0.0.4','0.3.2.0',theory(equality)]),
% 0.62/1.06 [pos('R.2','L')]).
% 0.62/1.06 cnf('1.0.0.6',plain,
% 0.62/1.06 ( $true ),
% 0.62/1.06 inference(trivial,[status(thm)],['1.0.0.5',theory(equality)]),
% 0.62/1.06 [conjecture_1]).
% 0.62/1.06
% 0.62/1.06 Proved Goals:
% 0.62/1.06 No. 1: join(meet(a,b),meet(a,c)) ?= meet(a,join(b,c)) joined, current: meet(a,join(c,b)) = meet(a,join(c,b))
% 0.62/1.06 1 goal was specified, which was proved.
% 0.62/1.06 % SZS output end CNFRefutation
% 0.62/1.06 #END OF PROOF
% 0.62/1.06
% 0.62/1.06 Problem WALDMEISTER_26129_n020
% 0.62/1.06 CPs.gen 16407
% 0.62/1.06 CPs.reexp 0
% 0.62/1.06 Select 557
% 0.62/1.06 R 152
% 0.62/1.06 E 6
% 0.62/1.06 vsize 6.5M
% 0.62/1.06 rss 3.8M
% 0.62/1.06 process.time 0.066s
% 0.62/1.06 wallclock.time 0.066s
% 0.62/1.06 status S
% 0.62/1.06
% 0.62/1.06
% 0.62/1.06 Waldmeister states: Goal proved.
% 0.62/1.06 % SZS status Unsatisfiable
%------------------------------------------------------------------------------